SH波对浅埋弹性圆柱及裂纹的散射与地震动
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摘要
采用Green函数、复变函数和多极坐标等方法研究含圆柱形弹性夹杂的弹性半空间中任意位置、任意方位有限长度裂纹对SH波的散射与地震动.构造了含圆柱形弹性夹杂的半空间对SH波的散射波,并求解了适合本问题Green函数,即含有圆柱形弹性夹杂的半空间内(表面)任意一点承受时间谐和的出平面线源载荷作用时位移函数的基本解答.利用裂纹"切割"方法在任意位置构造任意方位的裂纹,可以得到基体中圆柱形弹性夹杂和裂纹同时存在条件下的位移场与应力场.通过数值算例,讨论各种参数对夹杂上方地表位移的影响.
Scattering of SH wave and ground motion in an elastic half space containing an elastic cylindrical inclusion and a crack located at any position and direction are studied using Green's function,complex function and multi-polar coordinate system.A suitable Green's function is firstly constructed to obtain the fundamental solution of the displacement field for a half space(surface) with an elastic cylindrical inclusion.In addition, an out-plane harmonic line-source-loading is at an arbitrary point in half space.Meanwhile,a crack located at any position and direction can be built in half space with crack-division technique.The displacement field and stress field are obtained with elastic cylindrical inclusion and crack,and the ground motion above the elastic cylindrical inclusion is also discussed.
Scattering of SH wave and ground motion in an elastic half space containing an elastic cylindrical inclusion and a crack located at any position and direction are studied using Green's function,complex function and multi-polar coordinate system.A suitable Green's function is firstly constructed to obtain the fundamental solution of the displacement field for a half space(surface) with an elastic cylindrical inclusion.In addition, an out-plane harmonic line-source-loading is at an arbitrary point in half space.Meanwhile,a crack located at any position and direction can be built in half space with crack-division technique.The displacement field and stress field are obtained with elastic cylindrical inclusion and crack,and the ground motion above the elastic cylindrical inclusion is also discussed.
引文
1 Pao YH,Mow CC.Diffraction of Elastic Waves and Dynamic Stress Concentrations.Crane and Russak,New York,1973.114-304
2 Pao YH.Elastic wave in solids,ASME Trans.J Appl Mech, 1983,50:1152-1164
3黎在良,刘殿魁.固体中的波.北京:科学出版社,1995(Li Zailiang,Liu Diankui.Waves in Solids.Beijing:Science Press,1995(in Chinese))
4刘殿魁,刘宏伟.SH波散射与界面圆孔附近的动应力集中.力学学报,1998,30(5):597-604(Liu Diankui,Liu Hongwei. Scattering and dynamic stress concentration of SH-wave by interface circular hole.Acta Mechanica Sinica,1998,30(5): 597-604(in Chinese))
5何钟怡,樊洪明,刘有军.SH波绕界面孔的散射.力学学报, 2002,34(1):68-76(He Zhongyi,Fan Hongming,Liu Youjun. Scattering of SH-wave by an interface cavity.Acta Mechanica Sinica,2002,34(1):68-76(in Chinese))
6 Yang Zailin,Liu Dankui.Scattering far field solution of SH-wave by movable rigid cylindrical interface.Acta Mechanica Solida Sinica,2002,15(3):214-220
7 Liu Diankui,Shi Shouxia.The scattering of plane SH-wave by circular interface cavity with lining.Acta Mechanica Sinica,2002,34(5):796-802
8刘殿魁,林宏.SH波对双相介质界面附近圆形孔洞的散射.固体力学学报,2003,24(2):197-204(Liu Diankui,Lin Hong, Scattering of SH-waves by circular cavities near biomaterial interface.Acta Mechanica Solida Sinica,2003,24(2): 197-204(in Chinese))
9刘有军,何钟怡,樊洪明.弹性波绕任意形状界面孔的散射.固体力学学报,2005,26(1):92-96(Liu Youjun,He Zhongyi, Fan Hongming.Scattering of elastic wave by arbitrary interface cavity.Acta Mechanica Solida Sinica,2005,26(1): 92-96(in Chinese))
10刘殿魁,刘宏伟.孔边裂纹对SH波的散射及其动应力强度因子.力学学报,1999,31(3):292-299(Liu Diankui,Liu Hongwei.Scattering of SH-wave by crack originating at a circular hole edge and dynamic stress intensity factor.Acta Mechanica Sinica,1999,31(3):292-299(in Chinese))
11 Liu Diankui,Lin Hong.Scattering of SH-waves by an interface linear crack and a circular cavity near bimaterial interface.Acta Mechanica Sinica,2004,20(3):317-326
12 Liu Diankui,Chen Zhigang.Scattering of SH-wave by crack originating at an elliptic hole dynamic stress intensity factor.Applied Mathematics and Mechanics,2004,25(9): ??1047～1056
13陆建飞,陈章耀.折线型裂纹对SH波的动力响应,固体力学学报2004,25(3):315-319(Lu Jianfei,Chen Zhangyao. Dynamic response of a broken crack to SH waves.Acta Mechanica Solida Sinica,2004,25(3):315-319(in Chinese))
14陆建飞,蔡兰,柳春图.圆夹杂内裂纹对SH波的动力响应.力学学报,2003,9(35):623-627(Lu Jianfei,Cai Lan,Liu Chuntu.Scattering of SH wave by a crack in side a circular inclusion.Acta Mechanica Sinica 2003,9(35):623-627(in Chinese))
2 Pao YH.Elastic wave in solids,ASME Trans.J Appl Mech, 1983,50:1152-1164
3黎在良,刘殿魁.固体中的波.北京:科学出版社,1995(Li Zailiang,Liu Diankui.Waves in Solids.Beijing:Science Press,1995(in Chinese))
4刘殿魁,刘宏伟.SH波散射与界面圆孔附近的动应力集中.力学学报,1998,30(5):597-604(Liu Diankui,Liu Hongwei. Scattering and dynamic stress concentration of SH-wave by interface circular hole.Acta Mechanica Sinica,1998,30(5): 597-604(in Chinese))
5何钟怡,樊洪明,刘有军.SH波绕界面孔的散射.力学学报, 2002,34(1):68-76(He Zhongyi,Fan Hongming,Liu Youjun. Scattering of SH-wave by an interface cavity.Acta Mechanica Sinica,2002,34(1):68-76(in Chinese))
6 Yang Zailin,Liu Dankui.Scattering far field solution of SH-wave by movable rigid cylindrical interface.Acta Mechanica Solida Sinica,2002,15(3):214-220
7 Liu Diankui,Shi Shouxia.The scattering of plane SH-wave by circular interface cavity with lining.Acta Mechanica Sinica,2002,34(5):796-802
8刘殿魁,林宏.SH波对双相介质界面附近圆形孔洞的散射.固体力学学报,2003,24(2):197-204(Liu Diankui,Lin Hong, Scattering of SH-waves by circular cavities near biomaterial interface.Acta Mechanica Solida Sinica,2003,24(2): 197-204(in Chinese))
9刘有军,何钟怡,樊洪明.弹性波绕任意形状界面孔的散射.固体力学学报,2005,26(1):92-96(Liu Youjun,He Zhongyi, Fan Hongming.Scattering of elastic wave by arbitrary interface cavity.Acta Mechanica Solida Sinica,2005,26(1): 92-96(in Chinese))
10刘殿魁,刘宏伟.孔边裂纹对SH波的散射及其动应力强度因子.力学学报,1999,31(3):292-299(Liu Diankui,Liu Hongwei.Scattering of SH-wave by crack originating at a circular hole edge and dynamic stress intensity factor.Acta Mechanica Sinica,1999,31(3):292-299(in Chinese))
11 Liu Diankui,Lin Hong.Scattering of SH-waves by an interface linear crack and a circular cavity near bimaterial interface.Acta Mechanica Sinica,2004,20(3):317-326
12 Liu Diankui,Chen Zhigang.Scattering of SH-wave by crack originating at an elliptic hole dynamic stress intensity factor.Applied Mathematics and Mechanics,2004,25(9): ??1047～1056
13陆建飞,陈章耀.折线型裂纹对SH波的动力响应,固体力学学报2004,25(3):315-319(Lu Jianfei,Chen Zhangyao. Dynamic response of a broken crack to SH waves.Acta Mechanica Solida Sinica,2004,25(3):315-319(in Chinese))
14陆建飞,蔡兰,柳春图.圆夹杂内裂纹对SH波的动力响应.力学学报,2003,9(35):623-627(Lu Jianfei,Cai Lan,Liu Chuntu.Scattering of SH wave by a crack in side a circular inclusion.Acta Mechanica Sinica 2003,9(35):623-627(in Chinese))
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